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During a special sale, all video games cost $\$28$ and all movies cost $\$5$ . Hansen plans to spend some or all of his $\$120$ in birthday money on these movies and video games. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of video games Hansen can buy $\newline$ $y =$ the number of movies Hansen can buy $\newline$ $\newline$ Choices: $\newline$ (A) $28x + 5y \geq 120$ $\newline$ (B) $28x + 5y \geq 120$ $\newline$ (C) $28x - 5y \leq 120$ $\newline$ (D) $28x + 5y \leq 120$

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Write two-variable inequalities: word problems

Full solution

Q. During a special sale, all video games cost

\$28

and all movies cost

\$5

. Hansen plans to spend some or all of his

\$120

in birthday money on these movies and video games.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of video games Hansen can buy

\newline

y =

the number of movies Hansen can buy

\newline

\newline

Choices:

\newline

(A)

28x + 5y \geq 120

\newline

(B)

28x + 5y \geq 120

\newline

(C)

28x - 5y \leq 120

\newline

(D)

28x + 5y \leq 120

Calculate Video Games Cost: Determine the cost per item for video games and movies. Video games cost $\$28$ each, so the total cost for video games is $28$ times the number of video games Hansen buys, which is represented by the variable $x$ . Therefore, the cost for video games is $28x$ .
Calculate Movies Cost: Determine the cost per item for movies. Movies cost $\$5$ each, so the total cost for movies is $5$ times the number of movies Hansen buys, which is represented by the variable $y$ . Therefore, the cost for movies is $5y$ .
Combine Total Costs: Combine the costs for video games and movies to represent the total amount of money Hansen spends. The total cost is the sum of the cost of video games and the cost of movies, which is $28x + 5y$ .
Set Spending Limit: Hansen plans to spend some or all of his $\$120$ in birthday money. This means that the total cost of video games and movies must be less than or equal to $\$120$ . Therefore, the inequality that represents this situation is $28x + 5y \leq 120$ .

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